In computing, the modulo operation finds the remainder after division of one number by another (called the modulus of the operation).
Quotient (q) and remainder (r) as functions of dividend (a), using different algorithms
Given two positive numbers, a and n, a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
For example, the expression '5 mod 2' would evaluate to 1 because 5 divided by 2 has a quotient of 2 and a remainder of 1, while '9 mod 3' would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. (Doing the division with a calculator will not show the result referred to here by this operation; the quotient will be expressed as a decimal fraction.)
Although typically performed with a and n both being integers, many computing systems allow other types of numeric operands. The range of numbers for an integer modulo of n is 0 to n â 1. (a mod 1 is always 0; a mod 0 is undefined, possibly resulting in a division by zero error in programming languages.) See modular arithmetic for an older and related convention applied in number theory.
When either a or n is negative, the naive definition breaks down and programming languages differ in how these values are defined.
Remainder calculation for the modulo operation[edit]
In mathematics, the result of the modulo operation is the remainder of the Euclidean division. However, other conventions are possible. Computers and calculators have various ways of storing and representing numbers; thus their definition of the modulo operation depends on the programming language or the underlying hardware.
In nearly all computing systems, the quotientq and the remainder r of a divided by n satisfy Download buku ihya ulumuddin.
However, this still leaves a sign ambiguity if the remainder is nonzero: two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur. Usually, in number theory, the positive remainder is always chosen, but programming languages choose depending on the language and the signs of a or n.[6] Standard Pascal and ALGOL 68 give a positive remainder (or 0) even for negative divisors, and some programming languages, such as C90, leave it to the implementation when either of n or a is negative. See the table for details. a modulo 0 is undefined in most systems, although some do define it as a.
As described by Leijen,
Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by Knuth, is also a good definition. Despite its widespread use, truncated division is shown to be inferior to the other definitions.
ââDaan Leijen, Division and Modulus for Computer Scientists[10]
However, Boute concentrates on the properties of the modulo operation itself and does not rate the fact that the truncated division shows the symmetry (-a) div n = -(a div n) and a div (-n) = -(a div n), which is similar to the ordinary division. As neither floor division nor Euclidean division offer this symmetry, Boute's judgement is at least incomplete.[citation needed][original research?]
Common pitfalls[edit]
When the result of a modulo operation has the sign of the dividend, it can lead to surprising mistakes.
For example, to test if an integer is odd, one might be inclined to test if the remainder by 2 is equal to 1:
But in a language where modulo has the sign of the dividend, that is incorrect, because when n (the dividend) is negative and odd, n mod 2 returns â1, and the function returns false.
One correct alternative is to test that it is not 0 (because remainder 0 is the same regardless of the signs):
Or, by understanding in the first place that for any odd number, the modulo remainder may be either 1 or â1:
Notation[edit]
Some calculators have a mod() function button, and many programming languages have a similar function, expressed as mod(a, n), for example. Some also support expressions that use '%', 'mod', or 'Mod' as a modulo or remainder operator, such as
or
or equivalent, for environments lacking a mod() function ('int' inherently produces the truncated value of a/n)
How To Get Operator Mod On Bo4
Performance issues[edit]
Modulo operations might be implemented such that a division with a remainder is calculated each time. For special cases, on some hardware, faster alternatives exist. For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation:
Examples (assuming x is a positive integer):
In devices and software that implement bitwise operations more efficiently than modulo, these alternative forms can result in faster calculations.[11]
Optimizingcompilers may recognize expressions of the form
expression % constant where constant is a power of two and automatically implement them as expression & (constant-1) , allowing to write clearer code without compromising performance. This simple optimization is not possible for languages in which the result of the modulo operation has the sign of the dividend (including C), unless the dividend is of an unsigned integer type. This is because, if the dividend is negative, the modulo will be negative, whereas expression & (constant-1) will always be positive. For these languages, the equivalence x % 2n x < 0 ? x | ~(2n - 1) : x & (2n - 1) has to be used instead, expressed using bitwise OR, NOT and AND operations.
Equivalences[edit]
Some modulo operations can be factored or expanded similarly to other mathematical operations. This may be useful in cryptography proofs, such as the DiffieâHellman key exchange.
See also[edit]
Notes[edit]
References[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Modulo_operation&oldid=904560357'
Posted by8 months ago
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Not only are they insanely memey and fun to play with, but they are actually worth working for. I understand some people actually think some are overpowered but you have to realize you are giving up 2 class slots and 2 weapon attachments to use it. The use of an operator mod is a big sacrifice for a special attachment on the gun. People have to realize that it also has to do with the opponent you go against. If they are consistently wrecking you with the operator mod throughout the game, chances are they can wreck you without it. Overall, I think most are pretty balanced and are in a great place but I can understand how some people want certain attachments to be tweaked.
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Operator Mods are a new kind of attachment in Black Ops 4. These special attachments offer a unique bonus to the weapon. In order to equip an Operator Mod you must equip the Primary Operator Mod Wildcard for your Primary Weapon and/or the Secondary Operator Mod Wildcard for your Secondary Weapon. The Wildcards take a spot in your Pick 10, as do the Operator Mods.
Listed below, is every available Operator Mod in Call of Duty: Black Ops 4.
How To Get Operator Mod Strobe LightsOperator Mods[edit]
Comments
How can I calculate division and modulo for integer numbers in C#?
Peter Mortensen
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kartalkartal
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5 Answers
Before asking questions of this kind, please check MSDN documentation.
When you divide two integers, the result is always an integer. For example, the result of 7 / 3 is 2. To determine the remainder of 7 / 3, use the remainder operator (%).
Snak
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as-cii
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danodonovandanodonovan
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Fun fact!
The 'modulus' operation is defined as:
Ref:Modular Arithmetic
So you could roll your own, although it will be FAR slower than the built in % operator:
Edit: wow, misspoke rather badly here originally, thanks @joren for catching me
Now here I'm relying on the fact that division + cast-to-int in C# is equivalent to
Math.Floor (i.e., it drops the fraction), but a 'true' implementation would instead be something like:
In fact, you can see the differences between % and 'true modulus' with the following:
Results:
JerKimballJerKimball
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How To Get Operator Mod On Bo4
Division is performed using the
/ operator:
Modulo division is done using the Rion WilliamsRion Williams
% operator:
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Read two integers from the user. Then compute/display the remainder and quotient,
Peter Mortensen
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James DombroskiJames Dombroski
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